This section includes several notations that incorporate the Additive and Multiplicative Principles of Iconic Arithmetic. The image shows a ** Numerical Pocket Piece** from 1753. It shows the Table for Multiplication and Division (a modern times table) from 3 to 9 and is inscribed as “

*a new and short method*.” The times table for 2 is not included because doubling was taught as a necessary math skill, and was included in the algorithm for achieving multiplication and division.

## Section Contents

** Iconic arithmetic** defines addition and multiplication as physical activities.

** Unit-ensembles** are collections of identical sticks, pebbles, marks, tokens, or fingers.

** Depth-value notation** provides a convenient and simple way to group larger collections of units.

** Container numbers** illustrate unit-ensembles and depth-value working in concert.

** Parens notation** permits containers to be expressed by a string of typographical characters.

** Network numbers** express iconic arithmetic as composable networks.

** Block numbers** express iconic arithmetic as physical constructions using blocks.

** Spencer-Brown numbers** have units that act both as numbers and as operations.